On the nature of the coexistence surface and the critical double point in a polymer plus poor solvent system

We observe a critical double point (CDP) in a polystyrene (molecular weight=13 000) plus acetone mixture when a small amount of water is added to it instead of varying the molecular weight or the pressure. A very close access to CDP has been achieved, as exemplified by a sample with a miscibility gap, ΔTE (the difference between the upper and lower extremum temperatures, TEU and TEL, respectively) as small as 194 mK. The critical exponent (β) for the phase diagram exhibits a twofold increase in its 3-D Ising value for a sample with ΔTE=194 mK, when the usual field variable (the reduced temperature, t) is used. The universal value of β(=0.325) is retrieved for any ΔTE with the aid of the field variable tUL[=‖(TEU−T)(T−TEL) /TEU/BTEL‖]. Our evidence shows that, at least for the order parameter, ΔTE is preferable to ΔTc (the difference between the upper and lower critical temperatures, TU and TL, respectively) as a measure of the distance from CDP in this system. The critical line and the locus of the extremum temperatures are similar and are nearly parabolic in shape. Most of our observations can be understood in terms of the geometric picture of phase transitions as well as the Landau–Ginzburg theory, as applied to reentrant phase transitions. A microscopic understanding of the role of water in reducing the miscibility gap (ΔTE) in these complex systems remains to be achieved.